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# A basketball player is balancing a spinning basketball on the tip of his finger. The angular velocity of the ball slows down from 18.5 to 14.1 rad/s. During the slow-down, the angular displacement is 85.1 rad. Determine the time it takes for the ball to slow down.

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### Approach:

We are given initial velocity of the ball $(\omega_1)$,final velocity after slow-down $(\omega_2)$ and angular displacement $(\theta)$. To find the time it takes for the ball to slow down, we will use equation of rotational kinematics:

\begin{aligned} \theta&=\dfrac{1}{2} ( \omega+ \omega_0 )t \end{aligned}

where $\omega$ is final angular velocity, in our case equal to $\omega_1$, $\omega_0$ is initial angular velocity, in our case equal to $\omega_2$, and $t$ is time we are looking for.

### Given values:

$\omega_1=18.5 \ \tfrac{\text{rad}}{\text{s}}$

$\omega_2=14.1 \ \tfrac{\text{rad}}{\text{s}}$

$\theta=85.1 \ \text{rad}$

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